Troubleshooting measurement invariance in multigroup CFA: scaling techniques

CFA
1

I’m working on a multigroup CFA to check if latent factors are the same across three time points. My model has two latent factors and seven items. I’m running into some problems with the configural model and need advice.

First, when I use the marker variable method (fixing one loading at 1 and intercept at 0 for all groups), the model won’t converge. Any ideas why?

Second, I tried the ‘in every group’ method instead, setting latent variable means to 0 and variances to 1 across groups. This worked, but I’m not sure if it’s a good alternative. Should I stick with this or maybe try IRT for checking factor invariance?

Here’s a simplified version of what I’m trying:

* Method 1 (not converging)
sem (Factor1 -> item1 item2 item3) (Factor2 -> item4 item5) ///
    (item1 <- Factor1 _cons@0) (item4 <- Factor2 _cons@0), ///
    group(time) ginvariant(none) mean(Factor1 Factor2)

* Method 2 (works but unsure)
sem (Factor1 -> item1 item2 item3) (Factor2 -> item4 item5), ///
    group(time) ginvariant(none) variance(Factor1@1 Factor2@1) means(Factor1@0 Factor2@0)

What’s the best way to handle this? Thanks for any help!

2

I’ve encountered similar challenges with multigroup CFA models. In your case, the marker variable method’s convergence issues could stem from model misspecification or data peculiarities. Have you examined your data for multivariate normality and checked for any problematic patterns in your correlation matrices across time points?

Your second approach using the ‘in every group’ method is actually quite robust. It’s a valid alternative to the marker variable technique, especially when dealing with longitudinal data. This method often provides more stable estimates and can be less sensitive to potential measurement non-invariance.

One suggestion: consider implementing a stepwise approach to invariance testing. Start with configural invariance, then move to metric, scalar, and strict invariance. This systematic process can help pinpoint where exactly the model encounters issues.

Regarding IRT, while it’s a powerful tool, I’d recommend exhausting CFA options first. CFA is generally more straightforward for assessing factorial invariance across time points in your case.

Lastly, ensure your sample size is adequate for the complexity of your model. Insufficient power can lead to convergence problems and unstable estimates.

3

hey luke, been there with convergence probs. tried tweaking iteration limits? sometimes helps. ur 2nd method looks solid tho, pretty common for multiple timepoints. have u considered partial invariance? might help if full invariance is bein stubborn. also, hows ur sample size? uneven or small samples can mess things up. keep at it, youll crack it!

4

Hey Luke87! Interesting problem you’ve got there. I’ve run into similar issues before, and it can be super frustrating when models won’t converge.

For your first method, have you tried increasing the number of iterations or adjusting the convergence criteria? Sometimes that can help with stubborn models. Also, it might be worth checking if there are any extreme outliers in your data that could be causing issues.

Your second method seems like a solid alternative. Setting the latent means to 0 and variances to 1 is a common approach, especially when you’re dealing with multiple time points. It’s not inherently worse than the marker variable method, just different.

Have you considered trying a partial invariance approach? Sometimes relaxing a few constraints can help the model converge without compromising too much on the overall measurement invariance.

Oh, and about IRT - it’s definitely an option, but I’d probably exhaust the CFA approaches first. IRT can be great for item-level analysis, but it might be overkill if your CFA issues are solvable.

Quick question - how’s your sample size looking across the three time points? Uneven or small sample sizes can sometimes lead to convergence issues too.

Keep us posted on what works! This kind of stuff is always a bit of a puzzle, but that’s what makes it fun, right?